Irreconcilable differences? I disagree with your assertion. The court must find for a party un a business dispute involving property; NOT, subjectively prescribe an 'equitable] remedy. IF all things are equal THEN the court has NO premise to rule.
Delaware corporations are created by the State of Delaware. The Charter of every Delaware corporation says that its internal affairs are subject to the jurisdiction of the Delaware Court of Chancery (a court of equity).
The Delaware Corporation Law says that a corporation is to be managed by its Board of Directors and that, if the Board is hopelessly deadlocked, the Court of Chancery can resolve the deadlock. The statute provides a number of permissible remedies; forcing a sale is one of them.
This whole mess is the fault of the business owners: they set up a corporation with 50-50 voting control; did not create any mechanism for breaking a tie [something any decent corporate lawyer would have put into the by-laws]; got into a dispute, refuse to settle it, and neither one is willing to buy out the other.
So what is the court to do? Under Delaware law, nothing the corporation does is valid unless approved by the Board and the Board is incapable of functioning.